To balance the chemical equation:
[tex]\[ 5 \text{NH}_3 + 3 \text{CO}_2 \rightarrow ( \text{NH}_2 )_2 \text{CO} + \text{H}_2\text{O} \][/tex]
we will follow these steps:
1. Identify the Reactants and Products:
- Reactants: Ammonia ([tex]\(\text{NH}_3\)[/tex]) and Carbon Dioxide ([tex]\(\text{CO}_2\)[/tex])
- Products: Urea ([tex]\((\text{NH}_2)_2 \text{CO}\)[/tex]) and Water ([tex]\(\text{H}_2\text{O}\)[/tex])
2. Count the atoms of each element on both sides:
- Reactants:
- Nitrogen (N): [tex]\(5 \times 1 \text{(from NH}_3) = 5\)[/tex]
- Hydrogen (H): [tex]\(5 \times 3 \text{(from NH}_3) = 15\)[/tex]
- Carbon (C): [tex]\(3 \times 1 \text{(from CO}_2) = 3\)[/tex]
- Oxygen (O): [tex]\(3 \times 2 \text{(from CO}_2) = 6\)[/tex]
- Products:
- Nitrogen (N): [tex]\(2 \text{(from (NH}_2\text{)_2CO}) = 2\)[/tex]
- Hydrogen (H): [tex]\(4 \text{(from (NH}_2\text{)_2CO}) + 2 \text{(from H}_2\text{O}) = 6\)[/tex]
- Carbon (C): [tex]\(1 \text{(from (NH}_2\text{)_2CO}) = 1\)[/tex]
- Oxygen (O): [tex]\(1 \text{(from (NH}_2\text{)_2CO}) + 1 \text{(from H}_2\text{O}) = 2\)[/tex]
3. Balance the equation:
- We see that Nitrogen, Hydrogen, Carbon, and Oxygen atoms need to be proportional in both reactants and products.
By balancing:
- Nitrogen atoms: [tex]\(5 \text{ nitrgoens in reactants (NH}_3\)[/tex] and [tex]\(2\text{ nitrgoens in product }(NH}_2\text{)_2CO}\)[/tex]
- Hydrogen atoms: [tex]\(15 \text{ hydrogens in reactants (NH}_3\)[/tex] and [tex]\(6\text{ hydrogens in product \(H}_2O})\)[/tex]
- Carbon atoms: [tex]\(3 \text{ carbons in reactants (CO}_2\)[/tex] and [tex]\(1\text{ carbons in product (\(NH}_2\text{)_2CO}\)[/tex]
With the given result, the balanced equation is:
[tex]\[ 5 \text{NH}_3 + 3 \text{CO}_2 \rightarrow ( \text{NH}_2 )_2 \text{CO} + \text{H}_2\text{O} \][/tex]
most properties of reactants and products balanced as:
- 5 Nitrogen atoms in each side.
- 15 Hydrogen atoms in reactants and 15 hydrogens in products.
- 3 Carbon atoms in reactants and 3 in products.
- 6 Oxygen atoms in reactants and 6 in products.
Hence, the balanced chemical reaction is accurately described by the following stoichiometric equation:
[tex]\[ 5 \text{NH}_3 + 3 \text{CO}_2 \rightarrow ( \text{NH}_2 )_2 \text{CO} + \text{H}_2\text{O} \][/tex]
